On the message and time complexity of protocols for reliable broadcasts - Hong-Yi Tzeng
This paper presents a fundamental study on the message and time complexity of reliable broadcast/multicast protocols in point-to-point networks subject to omission failures. We assume a weakly synchronous model in which there is a known upper bound on the delay in delivering a message from one process to another. A faulty process may omit sending or receiving messages; this characterizes a common faulty behavior in networking applications. We focus our study on the number of messages and the maximum amount of time required of any fault-tolerant protocol in failure-free executions. We present protocols that, in an n-process network subject to at most t faulty processes, guarantee the delivery of a message from any process to all other nonfaulty processes. In particular, when no failure occurs in the network, our protocols require (n+t-1) messages and at most (n-1+upper bound [log2(t+1)])·δ units of time, where δ is the maximum time required to deliver a message from a process to another. Moreover, we show that our protocols are optimal with respect to message and time complexity. The new insights provided by the lower bound proofs yield a graph-theoretic characterization of all message and time optimal reliable broadcast/multicast protocols in failure-free executions. We further discuss the implications of our results on the support of multicast services in high-speed switching networks such as ATM
Keywords: ATM; LAN; Delay; Failure-free executions; Fault-tolerant protocol; Faulty behavior; Graph-theoretic characterization; High-speed switching networks; Lower bound; Message complexity; N-process network; Omission failures; Point-to-point networks; Reliable broadcast/multicast protocols; Time complexity; Upper bound; Weakly synchronous model